1. Introduction

Fiber-based refractive index (RI) sensors have been widely investigated in recent years. Various sensor heads based on special fiber structures, such as microstructured fibers [1], tilted fiber Bragg gratings [2, 3] interferometers [4], and long period fiber gratings (LPFGs) [5–8], have been proposed. Recently, high refractive index nano-film is combined with the sensor heads, which leads to the higher interaction of the evanescent field with the surrounding medium. The higher sensitivity could be expected [1, 2, 9, 10]. In this work, LPFGs are selected as the sensor head due to the advantages, such as simple structure, ease of fabrication, low insertion loss and low polarization-dependent. The LPFGs are intrinsically sensitive to the surrounding medium because they couple the core mode to the co-propagating cladding modes [5–7]. The LPFGs have the maximum index sensitivity when the surrounding refractive index (SRI) approaches the refractive index of the cladding [8]. When the LPFG is coated with a high index nano-film, the re-organization of the cladding modes occurs at a certain range of the SRI, which is called as transition region. Higher index sensitivity can be achieved and the sensitive region could be tuned as desired by changing the thickness of nano-film [9]. In previous studies, the majority of the attentions are paid on the sensitivity of the resonance wavelength to the SRI. For the conventional LPFGs, the grating contrast reduces remarkably. Even the grating dip vanishes as the SRI is close to the cladding index [10]. As a consequence, it is hard to detect the shift of the resonance wavelength.

There are two factors that may decrease the grating contrast sharply. One is the light scattering and material losses due to the deposition technologies such as electrostatic self-assembly (ESA) and Langmuir-Blodgett techniques [11, 12], the other is the transition of cladding modes. For the LPFGs coated with nano-film, as the SRI increasing, the lowest-order cladding mode becomes guided in the nano-film and the higher order cladding modes transmit to the adjacent lower modes. The grating coupling coefficient κ decreases sharply in the transition region, which causes the decrease of the grating contrast.

In this paper, we demonstrate the fabrication of the over-coupled LPFGs (OC-LPFGs) coated with high index Al₂O₃ nano-film. A new technology, atomic layer deposition (ALD) technology is utilized for the deposition of nano-film [13, 14]. ALD is a sequential self-limiting surface reacted chemical vapor deposition (CVD) process which can deposit atomic level films on the surface of fiber to produce uniform, smooth and precisely controlled coatings. So the light scattering due to the roughness of nano-film can be avoided [15, 16]. By using the OC-LPFGs, the higher grating contrast can be maintained when the grating coupling coefficient decreases in the transition region. We study the response of the resonance wavelength and grating contrast to the SRI changes for both the conventional LPFGs and the OC-LPFGs. The effect of the nano-film on the grating characteristics in the SRI sensitive region is investigated theoretically and experimentally. The modes transition is observed using an infrared camera, which is believed to be the first experimentally demonstration of the cladding mode transition for the LPFGs coated by the high index nano-film. A vectorial four-layer model is proposed to analyze the effective refractive index, field profile, cross-coupling coefficient and grating contrast of the nano-film coated LPFGs. The experimental results are well consistent with the theoretical analysis.

2. Theoretical analysis and simulation

Figure 1 shows the schematic diagram of the refractive index profile of the LPFG coated with high index nano-film. The four-layer cylindrical waveguide contains core, cladding, nano-film, and ambient. The LPFGs is coated by the AL₂O₃ nano-film with an approximate refractive index of 1.62 [17]. The theoretical model of the hybrid modes in four-layer cylindrical waveguide is established for the simulating of the grating characteristics. Firstly, the Debye potentials are solved from the Helmholtz equation; secondly, the vectors expressions of the electromagnetic field in the four layers are obtained using the relation between the electromagnetic field vectors and the Debye potentials; thirdly, the propagating constant of the cladding modes are gotten according to the boundary condition of continuity; lastly, the effective refractive index are obtained [18, 19]. The simulations were performed using MATLAB.

 

Fig. 1 The refractive index profile of the LPFG with the high index nano-film coating.

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Since the low dose of CO₂-laser radiation is used to write the LPFGs in the boron-doped fiber, only azimuthally symmetric index change occurs in the cross-section of the fiber [20], consequently transmission spectrum of the LPFG only contains the attenuation dips which arise from the coupling between core mode and azimuthally symmetric cladding modes [9, 21, 22]. Therefore, only HE_1,j and EH_1,j modes need to be considered.

The field distribution of the cladding modes is strongly dependent on the features of the nano-film (refractive index and thickness) and the SRI. Figure 2 shows the simulated effective refractive index of the first 13 grating cladding modes as a function of the SRI when the thickness of the nano-film is 100 nm, 200 nm and 300nm, respectively. For a fixed nano-film thickness and refractive index, the effective index of cladding modes goes up as the SRI increasing. At a particular value of the SRI, the effective index of the lowest order cladding mode (HE_1,2) exceeds that of the cladding material so that the HE_1,2 mode is guided into the nano-film. At the same time the higher order cladding mode HE_1,j (j>2) transmits to the adjacent lower cladding mode EH_1,j-1, and then transmits to the more lower cladding mode HE_1,j-2 after a short SRI interval. The two-step transition of the effective refractive index of cladding modes as a function of the SRI is depicted in Fig. 2 (d) [10]. It can be seen that the effective refractive index change sharply in the transition region, where the reorganization of cladding modes occurs. With the increasing of the nano-film thickness, the transition region moves to the region with lower SRI [21].

 

Fig. 2 Effective refractive index of the first 13 cladding modes as a function of the SRI when the thickness of the nano-film is (a) 100 nm, (b) 200 nm and (c) 300nm. (d) The detail view for the two-step transition of cladding modes.

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According to the phase matching condition, the resonance wavelengths of the cladding modes shift dramatically in the transition region, as shown in Fig. 3. The sensitivity of the resonance wavelength to the SRI improves significantly.

 

Fig. 3 Response of the resonance wavelength to SRI for different nano-film thickness

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Figure 4 shows the radial electric fields of the HE_1,14 at resonance wavelength under a series of SRI values with tiny interval. It is found that the radial electric field of the HE_1,14 maintains the original field profile (SRI is 1.33) in the transition region. It is in accordance with Villar’s reports that there is a one-step transition for higher-order cladding modes [10].

 

Fig. 4 (a) n²(r) times the radial electric field of the HE_1,14, EH_1,13, HE_1,12 mode at SRI 1.33, (b) n²(r) times the radial electric field of the HE_1,14 mode under a series of SRI values when the thickness of the nano-film coating is 100 nm.

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According to the coupled mode theory, the cross coupling coefficient between the core mode and the ith order cladding mode can be expressed as [5]:

Where ${\epsilon }_0$ is the free space permittivity, $E_r^{co}$, $E_{\varphi }^{co}$ are the radial electric field and the tangential electric field for the core mode, $E_r^{cl}$, $E_{\varphi }^{cl}$ are for the HE or EH modes of the cladding modes. $\sigma (z)=\Delta n/2n_1$, where $\Delta n$is the variation of the refractive index modulation.

When the SRI is 1.33, the cross coupling coefficients of the HE modes are much larger than that of the EH modes. For comparison, the coupling coefficients of HE_1,14 and EH_1,13 are simulated, as shown in Fig. 5. As the SRI increases, the cross coupling coefficients of the HE_1,14 at resonance wavelength decreases monotonously at first and then increases in the transition region. However, the variation of the cross coupling coefficients of the EH_1,13 at resonance wavelength performs different trend. As the SRI increasing, the cross coupling coefficients of the EH_1,13 at resonance wavelength increases monotonously at first and then decreases in the transition region. The value of the HE mode is much larger than that of the EH mode. The cross coupling coefficients of the HE mode in the conventional LPFGs are smaller than that in the OC-LPFGs. Therefore, the conventional LPFGs and the OC-LPFGs have the similar variation trend in terms of the effective refractive index, the resonance wavelength and the cross coupling coefficient.

 

Fig. 5 Cross coupling coefficient for HE_1,14 and EH_1,13 modes as a function of the SRI when the nano-film are (a) 100 nm thickness in the conventional and OC-LPFGs, (b) 200 nm thickness in the conventional and OC-LPFGs

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The grating contrast corresponding to the coupling between the core mode and the ith cladding mode can be approximately expressed as [23]

Figure 6 shows the grating contrast of the HE_1,14 modes versus SRI for the conventional LPFGs and the OC-LPFGs coated by nano-film with different thickness. For the conventional LPFG, the grating contrast decreases as the SRI increasing before the transition and then fluctuates in the transition region. For the OC-LPFGs, the grating contrast increases as the SRI increasing before the transition and then fluctuates in the transition region. The grating contrast of the OC-LPFGs is always larger than that of the conventional LPFGs in all the SRI range.

 

Fig. 6 The grating contrast of the HE_1,14, modes versus SRI for the conventional LPFGs and the OC-LPFGs when the thickness of the nano-film coating is (a) 100 nm, (b) 200 nm, (c) 300 nm

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3. Experimental results and discussion

To fabricate the LPFGs, a focused pulsed CO₂ laser was used as the writing source, which can be computer-programmed [20]. The LPFGs used in the experiment were fabricated in a commercial boron-doped fiber (Fibercore PS 1250/1500). The grating has a pitch of 300 μm and period number of 60. The grating length is 1.8 cm. In order to monitor the dynamics of the grating writing process, a broadband light source and an optical spectrum analyzer (OSA, AQ6375) were used to measure the transmission spectra of the LPFGs. The resonance wavelengths and the grating contrasts were measured after every scanning cycle of the CO₂ laser. To fabricate the conventional LPFG, the scanning of the CO₂ laser was stopped when the grating contrast reached the maximum. The grating contrast will decrease if the laser scanning further continues. The OC-LPFGs with κL>π/2 can be fabricated. To guarantee the comparability of the conventional LPFG and the OC-LPFG, the same parameters including the periods, the lengths, and the contrasts of the gratings were selected.

For the deposition of the Al₂O₃ nano-film along the grating, the ALD equipment (TFS 200, BeneQ) was utilized. The LPFGs were placed in the cylindrical reaction chamber with a diameter of 22 cm and a height of 3 cm. Firstly, two precursors (TMA (Al(CH₃)₃) and O₃) and N₂ gas were valve controlled and purged into the heated reacting chamber. The purged order is TMA-N₂-O₃-N₂. The chemical reaction formula is 4Al(CH₃)₃ + 3O₂ →2Al₂O₃ + 6C₂H₆. The deposition temperature was kept at 210 °C. One reactive cycle was completed in 2 seconds, after that a monolayer Al₂O₃ with about 0.1 nm thickness was deposited on the LPFG [15]. The thicknesses of the AL₂O₃ nano-films with 3000 deposition cycles have been measured at the fiber cross-section using the scanning electron microscope (SEM, Hitachi SU8220). The mean thickness and the standard deviation of the film thicknesses are 269.375nm and 4.3439nm, respectively. It is proved that ALD technology guaranteed the Al₂O₃ nano-film to have the smooth surfaces and good uniformity. The SEM pictures are shown in Fig. 7.

 

Fig. 7 (a) is the SEM picture of the cross section of the coated LPFG and (b), (c), (d), and (e) are the magnification of the segments corresponding to the positions marked with red circles on (a).

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The transmission spectra and index characteristics of the LPFGs coated with high index nano-film were investigated experimentally. Figure 8 shows the resonance wavelength shift and the contrast variation of the HE_1,14 mode before and after nano-film coating in the conventional LPFG and the OC-LPFG at a SRI of 1.33. The resonance wavelengths of the LPFGs have blue shift after the nano-film coating. The grating contrast of the conventional LPFG coated with nano-film decreases while the contrast of the OC-LPFG increases after nano-film coating.

 

Fig. 8 The transmission spectra of (a) the conventional LPFG and (b) the OC-LPFG before and after nano-film coating.

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Figure 9 shows the dependence of the resonance wavelength shift of the HE_1,14 modes on SRI. It can be seen that the experimental results are consistent with the simulation results. When the SRI changed in the index range 1.4426-1.4524, which is approaching the cladding index, the resonance wavelength of the HE_1,14 had a blue shift with a maximum sensitivity of 970 nm/RIU for a bare LPFG. The attenuation dip vanished when the SRI further increases. For the LPFG coated with 100 nm-thickness nano-film, the transition region was approximately in the range 1.437-1.461, the sensitivity of the resonance wavelength to SRI reached up to 3000 nm/RIU. It is worth noting that, when SRI was changed in the range 1.4524-1.461, the attenuation dip of bare LPFG vanished, but the resonance wavelength of the coated OC-LPFGs was still sensitive to the SRI, as shown in Fig. 10. The dynamic range of refractive index measurement increased after nano-film coating. For the LPFG coated with 200 nm-thickness nano-film, the transition region shifted to the index range 1.3622-1.39 approximately. The measured index sensitivity was 1500 nm/RIU. For the gratings coated with 300 nm-thickness nano-film, the resonance wavelength shift was much smaller in the range 1.33-1.461, which can be attributed to that the transition region moved to the region far less than 1.33.

 

Fig. 9 The dependence of the resonance wavelength shift of the HE_1,14, modes on SRI. (a) the conventional LPFG coated by nano-film with a thicknesses of 0, 100 nm, 200 nm and 300 nm, (b) the OC-LPFG coated by nano-film with a thicknesses of 0, 100 nm, 200 nm and 300 nm.

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Fig. 10 The transmission spectra of (a) the conventional bare LPFG and (b) the OC-LPFG coated with 100 nm nano-film at a SRI of 1.4524 and 1.461.

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Figure 11 shows the dependence of the contrast variation of the HE_{1, 14} mode on SRI for the conventional and OC-LPFGs coated by nano-film with different thickness. The grating contrast of the LPFGs at the SRI of 1.33 was used as the reference.

 

Fig. 11 The dependence of the contrast variation of the HE_1,14 mode on SRI. (a), (c) are for the conventional LPFG with 100 nm, 200 nm respectively, and (b), (d) are the OC-LPFG with 100 nm, 200 nm nano-film respectively.

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For conventional LPFGs, the grating contrast decreased as the SRI increased before the transition region due to the decrease of the cross coupling coefficient. For OC-LPFGs, the grating contrast increased with the SRI although the cross coupling coefficient decreased. However, in the transition region, the contrast of both OC-LPFGs and conventional LPFGs decreases at first and then increases in the transition region. It can be attributed to the mode transition, as depicted in the reference [10]. Even though it seems that there is a one-step transition for higher-order mode resonances, the presence of EH modes plays an important role. The contrast of the HE_{1, 14} mode trends to that of the EH_{1, 13} mode at first and then to that of the HE_1,12 mode. Moreover, it could be found that the OC-LPFGs permitted to obtain a higher grating contrast in the transition region compared with the conventional LPFGs, which is helpful for the wavelength detection.

To confirm the mode transition, the near-field patterns of the HE_1,14 mode were taken continuously by an infrared camera (Model C10633-23 from Hamamatsu Photonics) at the resonance wavelength at different ambient index. Transmission spectra of the OC-LPFG coated with 100 nm nano-film at four SRI of 1.33, 1.426, 1.443, and 1.461 are shown in Fig. 12. When the SRI increases, the original dip (HE_1,14 mode) at 1510 nm shifts towards shorter wavelength ~1350 nm. After the mode transition at high SRI, the original dip (original HE_1,16 mode) at longer wavelength shifts to the wavelength ~1550 nm, which transits to be the HE_1,14 mode. Figure 12 (a) shows the near-field patterns corresponding to the attenuation dip at 1510 nm when the SRI was 1.33 (before the transition region). The cladding mode was identified to be HE_1,14 mode. Figure 12 (b) shows the near-field patterns corresponding to the attenuation dip at 1550 nm when the SRI was 1.461 (after the transition region), which is the same as that of the HE_1,14 mode. It indicated that the HE_1,16 mode did transit to the HE_1,14 mode in the transition region. Moreover, it can be proved that the near-field pattern of the HE_1,14 mode coincides with that of the LP₀₈ mode. It can be believed that this is the first experimental demonstration of the cladding mode transition of the coated LPFGs with increasing SRI.

 

Fig. 12 The transmission spectra of the LPFG coated with 100 nm nano-film at four SRI values. (a) the near-field patterns corresponding to the attenuation dip at 1510 nm when the SRI was 1.33 and (b) the-field patterns corresponding to the attenuation dip at 1550 nm when the SRI was 1.461

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4. Conclusion

In this paper, we demonstrated the coating of the LPFGs with high index nano-film using the ALD technology. When the nano-film with 100 nm thickness was deposited on the grating, the high index sensitivity of 3000 nm/RIU was obtained. The index sensitive region was expanded to the index up to 1.461, which is in the blind detecting areas of the bare LPFG. The contrast of the OC-LPFGs and conventional LPFGs were measured and the OC-LPFGs permitted to obtain a higher grating contrast in the transition region. The cladding modes transition was observed experimentally by infrared camera. The theoretical model of the hybrid modes in four-layer cylindrical waveguide was proposed for numerical simulation.